document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123419>Question 1123419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if two vertices of an equilateral triangle are (-4,-3) and(4,1), find the remaining vertex\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739738 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two solutions (corresponding to points C and D) as shown in the drawing below.   \r<BR>\n" );
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document.write( "Line AB has the equation  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%281%2F2%29x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+%281%2F2%29x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Line CD has the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-2x+-+1+ ALIGN=MIDDLE  ALT=\"+y+=+-2x+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+abs%28AB%29%5E2+=+%284-%28-4%29%29%5E2+%2B+%281-%28-3%29%29%5E2+=+64%2B16+=+80+ ALIGN=MIDDLE  ALT=\"+abs%28AB%29%5E2+=+%284-%28-4%29%29%5E2+%2B+%281-%28-3%29%29%5E2+=+64%2B16+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using point C(Cx, Cy), the distance squared to C from B  (and A) must be  80.  Using B's coordinates:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28Cx-4%29%5E2+%2B+%28Cy-1%29%5E2+=+80+ ALIGN=MIDDLE  ALT=\"+%28Cx-4%29%5E2+%2B+%28Cy-1%29%5E2+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%28Cx%5E2-8Cx%2B16%29+%2B+%28Cy%5E2-2Cy%2B1%29+=+80+ ALIGN=MIDDLE  ALT=\"++%28Cx%5E2-8Cx%2B16%29+%2B+%28Cy%5E2-2Cy%2B1%29+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subs <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Cy+=+-2Cx+-+1+ ALIGN=MIDDLE  ALT=\"+Cy+=+-2Cx+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Cy%5E2+=+4Cx%5E2+%2B+4Cx+%2B1 ALIGN=MIDDLE  ALT=\"Cy%5E2+=+4Cx%5E2+%2B+4Cx+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28Cx%5E2-8Cx%2B16%29+%2B+%284Cx%5E2%2B4Cx%2B1%29+%2B+%284Cx+%2B+2%29+%2B+1+=+80+ ALIGN=MIDDLE  ALT=\"+%28Cx%5E2-8Cx%2B16%29+%2B+%284Cx%5E2%2B4Cx%2B1%29+%2B+%284Cx+%2B+2%29+%2B+1+=+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which resolves to   C at  (  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-4%2Asqrt%283%29%29-1++ ALIGN=MIDDLE  ALT=\"+%28-4%2Asqrt%283%29%29-1++\"   DISABLED_style= \"max-width:90%; height:auto;\" > )        <br>\r<BR>\n" );
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document.write( "and   D at  (  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"-2%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284%2Asqrt%283%29%29-1++ ALIGN=MIDDLE  ALT=\"+%284%2Asqrt%283%29%29-1++\"   DISABLED_style= \"max-width:90%; height:auto;\" > )        <br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28500%2C500%2C+-10%2C10%2C+-10%2C+10%2C+grid%280%29%2C%0D%0A+++++++line%28-4%2C-3%2C+4%2C+1%29%2C%0D%0A+++++++blue%28circle%28-4%2C-3%2C8.944%29%29%2C%0D%0A+++++++green%28circle%284%2C1%2C+8.944%29%29%2C%0D%0A+++++++line%28-3.464%2C+5.928%2C+3.464%2C+-7.928%29%2C%0D%0A++++++++line%284%2C1%2C+3.464%2C+-7.928%29%2C%0D%0A++line%28-3.464%2C+5.928%2C+4%2C1%29%2C%0D%0A++line%28-3.464%2C+5.928%2C+-4%2C-3%29%2C%0D%0A++line%28-4%2C-3%2C+3.464%2C+-7.928%29%2C%0D%0A++locate%28-6%2C-3%2C+%22A%28-4%2C-3%29%22%29%2C%0D%0A++locate%284.5%2C1.5%2C+%22B%284%2C1%29%22%29%2C%0D%0A%0D%0A+++++++locate%28-3.6%2C6.5%2C+%22D%22%29%2C%0D%0A%0D%0A+++++++locate%283.6%2C-7.8%2C+%22C%22%29%0D%0A%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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